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《Mathematics in Practice and Theory》 2008-21
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An Inequality on Non-negative Matrix

HUANG Ke-weng(Jinhua College of Profession and Technology,Jinhua Zhejiang 321017,China)  
In this note,we prove:if X=(xij)is an m×n matrix with non-negative real entries,which are not all equal to 0,then for 0p1,the following inequality holds:(m~(p-1)sum from i=1 to m ( ) r_i~p+n~(p-1) sum form j=1 to n ( ) c_j~p)/sum form to i=1 to m ( ) sum form to j=1 to n ( ) x_(ij)~p+(mn)~(p-1) sum form to i=1 to m ( ) sum form to j=1 to n ( )x_(ij)~p ≤m~(p-1)+n~(p-1)/(mn)~(p-1)+min(m~(p-1)),n~(p-1),Our theorem complements a result of Xiaojing Yang [Linear Algebra Appl,2002,348,41-47],who proved the converse of the inequality for p≥1.
【CateGory Index】: O151.21
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